Selection on complex characters is an important process in essentially every biological system. Many of the human traits that are important to the health sciences result from complicated interactions among multiple genes and the environment. In addition, selection (artificial and natural) on pathogens has recently become a very important topic (e.g., antibiotic resistance in bacteria, viral evolution within a host). The tools of quantitative genetics permit reconstruction of the selective history (and prediction of the future response to selection) for a phenotype comprised of multiple complex traits. However, this endeavor rests on the critical and controversial assumption that the genetic variance-covariance matrix (G- matrix) remains constant during the time period of interest. Empirical and theoretical studies have been devoted to this stability issue, but it remains unresolved. Simulation-based models have been applied successfully to other aspects of quantitative genetic theory, but never to the evolution of the G-matrix. Thus, the goal of this project is to use computer simulations to investigate the conditions that promote G-matrix stability and instability. Dynamics of the G-matrix will be investigated under stabilizing and directional selection, and the results will be important for the application of quantitative genetics to a broad array of biological disciplines, including the health sciences and evolutionary biology.